1. What is the Velocity at Any Radius Formula?

The velocity at any radius formula calculates the velocity of fluid at a specific radial position in a pipe, given the maximum velocity and pipe dimensions. This formula is derived from the parabolic velocity profile of laminar flow in circular pipes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Velocity of Fluid (m/s)
• \( V_m \) — Maximum Velocity (m/s)
• \( r_p \) — Radius of Pipe (m)
• \( d_o \) — Pipe Diameter (m)

Explanation: The formula describes a parabolic velocity distribution where velocity is maximum at the center (r=0) and zero at the pipe wall (r=d_o/2).

3. Importance of Velocity Calculation

Details: Understanding velocity distribution in pipes is crucial for fluid dynamics analysis, pipe design, flow rate calculations, and predicting pressure drops in fluid systems.

4. Using the Calculator

Tips: Enter maximum velocity in m/s, radius of pipe in meters, and pipe diameter in meters. All values must be positive, and the radius should not exceed half the pipe diameter.

5. Frequently Asked Questions (FAQ)

Q1: What type of flow does this formula apply to?
A: This formula applies specifically to laminar flow in circular pipes where the flow is fully developed and steady.

Q2: What happens if the radius exceeds half the pipe diameter?
A: The radius should always be ≤ half the pipe diameter. If r_p > d_o/2, the calculation would give negative velocity, which is physically impossible.

Q3: How is maximum velocity related to average velocity?
A: For laminar flow in circular pipes, maximum velocity is exactly twice the average velocity (V_m = 2V_avg).

Q4: Does this formula work for turbulent flow?
A: No, this parabolic distribution is specific to laminar flow. Turbulent flow has a different velocity profile that is flatter near the center.

Q5: What are typical units for these measurements?
A: While meters and m/s are standard, any consistent unit system can be used as long as all inputs use the same units.